1 . 已知椭圆
,点
在椭圆上,如图,用
表示椭圆在点
处切线的单位向量.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
,求
的最大值;
(2)是否存在定圆
,使得圆
的任一切线与
的交点
满足
,若存在,求出圆
方程,若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a6e483672a226118dff5a39aa28449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4fbb5a4568dd3e4baec9f8358552b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e8744362c6e224146461b97faf9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75874285daf265905257368573ded035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a21698cc2ceabd28d995692ab2bfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2 . 已知直线
与曲线
交于
、
两点,
为坐标原点.
(1)当
时,有
,求曲线
的方程;
(2)当实数
为何值时,对任意
,都有
为定值
?指出
的值;
(3)已知点
,当
,
变化时,动点
满足
,求动点
的纵坐标的变化范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b8496f1a8c16c4aea19b106352e026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5817f67625f677f1a8c35b20c0c6aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0f4a227754facf7d5aee67d230c0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0ba14e41e306e5633ad4bf1cdedd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b624d88827e92e12bc0a8f1067cbe72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c560c2606753f8cafa92eacc2dc75ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-01-19更新
|
383次组卷
|
2卷引用:上海市格致中学2021届高三上学期10月月考数学试题
名校
解题方法
3 . 已知椭圆E中心在坐标原点,方程为
,直线
与椭圆交于A、B两点.
(1)当k=1时,若椭圆E上存在点C使得点O、A、C、B构成平行四边形OACB,求直线
方程;
(2)若直线
过左焦点F(不与x轴重合),弦AB中点为点P,过F作
的垂线
,且直线
与直线OP交于点G,求点G所在的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
(1)当k=1时,若椭圆E上存在点C使得点O、A、C、B构成平行四边形OACB,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
2021-08-17更新
|
267次组卷
|
2卷引用:江苏省泰州市姜堰中学2020-2021学年高二上学期12月月考数学试题
解题方法
4 . 直线与
轴交于点
,与
轴交于点
,且直线与椭圆
相切,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7a6fd6d651ae341154c2e40928d628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eb5be422dc9f0f01736b0f2b08a3a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次